An Active Set Method in Image Inpainting

In this paper, we apply a semismooth active set method to image inpainting. The method exploits primal and dual features of a proposed regularized total variation model, following after the technique presented in [4]. Numerical results show that the method is fast and efficient in inpainting sufficiently thin domains.

• Marrick Neri
• Esmeraldo Ronnie Rey Zara

• Active set method
• image inpainting
• total variation model.

[1] M. Bertalmio, G. Sapiro, C. Ballester,"Image inpainting,”in Proceedings of SIGGRAPH 2000, New Orleans, LA (2000).
[2] T. Chan, J. Shen, "Mathematical models for local nontextureinpaintings,” SIAM J. Appl. Math. Math. 62(3), 1019-1043, (2002).
[3] M. Hintermüller, K. Ito, K. Kunisch, "A primal-dual active set strategyas a semismooth Newton method,” SIAM J. Opt. 13(3), 865-888 (2003).
[4] M. Hintermüller, G. Stadler, "An infeasible primal-dual algorithmfor total bounded variation-based inf-convolution-tye image restoration," SIAM J. Sci. Comput. 28(1), 1--23 (2006).
[5] I. Ekeland, R. Temam, Convex analysis and variational problems. North Holland, Amsterdam (1976).